We study the dynamics of (i) neutral test particles, (ii) magnetically charged test particles, and (iii) test magnetic dipole around a regular Bardeen black hole surrounded by perfect fluid dark matter (PFDM). It has been shown how the magnetic charge of the black hole and the parameter of the surrounding PFDM can influence the innermost stable circular orbit (ISCO) radius of a test particle. We have found that the ISCO radius is strongly affected as a consequence of the combined effect of the magnetic charge parameter and the perfect fluid dark matter. The black hole magnetic charge parameter $g$ and the combined effect of perfect fluid dark matter can mimic the black hole rotation parameter up to $a/M\approx 0.9$. It has been observed that the ISCO for magnetic dipole disappears at the values exceeding the calculated upper value for the magnetic interaction parameter $\beta$. The upper limit decreases with the increase of both the dark matter and magnetic charge parameters. Finally, as an astrophysical application, we have analyzed degeneracy effects of spin of Kerr black holes and magnetic charge of regular Bardeen black holes for the different values of the dark matter parameter providing exactly the same value for ISCO radius of a magnetic dipole with the same value of the parameter $\beta =10.2$ of the magnetar called PSR J1745-2900 orbiting around supermassive black hole Sagittarius A*. It has been observed that the magnetic charge of the pure regular Bardeen black hole can mimic the spin of a Kerr black hole up to $a/M\simeq 0.8085$, while upper limit for the magnetic charge which may provide ISCO for the magnetic dipole is $g_{\text{upper}}\simeq 0.65M$. In the presence of PFDM with the parameter $\alpha =0.01(0.05)$, the upper limit for the magnetic charge decreases and equals to $g_{\text{upper}}\simeq 0.62M$ ($0.548M$) and consequently mimicker value for the spin parameter of black hole lies in the range of $a/M\in (0.0106÷0.8231)$ ($a/M\in (0.0816÷0.8595)$). We also show that the same values of the spin of Kerr black hole and the magnetic charge of regular Bardeen black hole surrounded by PFDM provide the same values for the ISCO radius of the chosen magnetar.

We investigate the dynamics of neutral and charged test particles around axially symmetric magnetized black hole spacetime. We consider its electromagnetic field in the black hole vicinity and study its impact on the dynamics of test particles. We determine the radius of the innermost stable circular orbit (ISCO) for neutral and charged test particles and show that the combined effect of black hole electric charge and magnetic field strongly affects the ISCO radius, thus shrinking its values. We also show that the ISCO radius of positively (negatively) charged particle initially gets increased (decreased) and then gets radically altered with an increase in the value of both black hole electric charge and test particle charge. It turns out that the repulsive (attractive) Coulomb force dominates over the Lorentz force arising from the black hole magnetic field. Typically, black hole rotation causes axially symmetric spacetime case. Similarly, it turns out that a magnetized black hole solution also causes axially symmetric spacetime as a consequence of the presence of magnetic field. We study a degeneracy for the value of the ISCO between the Kerr and the magnetized Reissner-Nordström black hole geometries and show that the combined effects of black hole charge and magnetic field can be mimicked by Kerr spacetime with the spin parameter up to $a/M\approx 0.8$. Finally, we consider the center of mass energy of colliding particles and show that an increase in the values of black hole magnetic field and electric charge leads to high center of mass energy extracted by collision of two particles.

We study the motion of electrically charged particles, magnetic monopoles, and magnetic dipoles around electrically and magnetically charged stringy black holes. From the analysis of the radius of the innermost stable circular orbit of electrically charged particles, we show that the electric charge $Q$ of stringy black holes can mimic well the spin of Kerr black holes; the black hole magnetic charge $Q_m$ can mimic spins up to $a_{*}\simeq 0.85$ for magnetic dipoles; the magnetic charge parameter $g$ of a magnetic monopole can mimic spins up to $a_{*}\simeq 0.8$. This is due to the destructive character of the magnetic field, and such a result excludes the existence of an appreciable black hole magnetic charge in astrophysical black holes from the observation of rapidly rotating objects with dimensionless spin up to $a_{*}\simeq 0.99$. We then consider the magnetar SGR (PSR) J1745-2900 as a magnetic dipole orbiting the supermassive black hole Sagittarius A* (Sgr A*). We show that Sgr A* may be interpreted as a stringy black hole with magnetic charge $Q_m/M\le 0.4118$.

We study the motion of test particles and photons in the vicinity of the (2+1)-dimensional Gauss–Bonnet (GB) BTZ black hole. We find that the presence of the coupling constant serves as an attractive gravitational charge, shifting the innermost stable circular orbits outward with respect to the one for this theory in four dimensions. Further, we consider the gravitational lensing, to test the GB gravity in (2+1) dimensions and show that the presence of the GB parameter causes the bending angle to first increase with the increase in the inverse of the closest approach distance, $$u_0$$u0 , reaching a peak value for a specific $$u_0^*$$u0∗ , and then decreasing to zero. We also show that the increase in the value of the GB parameter decreases the bending angle, and the increase in the absolute value of the negative cosmological constant produces an opposite effect on this angle.

The thermal radiation properties of the accretion disk around a non-rotating black hole with a perfect fluid dark matter (PFDM) environment are investigated. A non-rotating black hole surrounded by perfect fluid dark matter together with a classical geometrically thin but optically thick Novikov–Thorne disk is selected as a system to be analyzed. It is observed that the perfect fluid dark matter strengthens the gravitational field, which leads to both the increase of the radii of the event horizon and the innermost stable circular orbit (ISCO). However, for the flux of the radiant energy over the accretion disk, the maximum flux is reduced and shifted outwards the central object under the influence of the perfect fluid dark matter. The dependence of the thermal profile of the disk on the radial coordinate and the intensity of perfect fluid dark matter shows analogous behavior. It has been demonstrated that the radiative efficiency of the accretion disk is increased from ∼6% up to ∼20% with the increase in the intensity of the surrounding perfect fluid dark matter. The thermal spectra of the accretion disk has also been explored, which is shifted towards the lower frequencies (corresponding to the gravitational redshift of the electromagnetic radiation coming from the disk) with the increase in the intensity of the perfect fluid dark matter.

In the present paper, we have investigated the motion of charged particles together with magnetic dipoles to determine how well the spacetime deviation parameter $$\epsilon $$ϵ and external uniform magnetic field can mimic the spin of a rotating Kerr black hole. Investigation of charged particle motion has shown that the deviation parameter $$\epsilon $$ϵ in the absence of an external magnetic fields can mimic the rotation parameter of the Kerr spacetime up to $$a/M \approx 0.5$$a / M ≈ 0.5 . The combination of an external magnetic field and deviation parameter can do even a better job mimicking the rotation parameter up to $$a/M\simeq 0.93$$a / M ≃ 0.93 , which corresponds to the rapidly rotating case. Study of the dynamics of the magnetic dipoles around quasi-Schwarzschild black holes in the external magnetic field has shown that there are degeneracy values of the ISCO radius of test particles at $$\epsilon _{cr}>\epsilon \ge 0.35$$ϵ cr > ϵ ≥ 0.35 which may lead to two different values of the innermost stable circular orbit (ISCO) radius. When the deviation parameter is in the range of $$\epsilon \in (-1,\ 1)$$ϵ ∈ ( - 1 , 1 ) , it can mimic the spin of a rotating Kerr black hole in the range $$a/M \in (0.0537, \ 0.3952)$$a / M ∈ ( 0.0537 , 0.3952 ) for magnetic dipoles with values of the magnetic coupling parameter $$\beta \in [-0.25,\ 0.25]$$β ∈ [ - 0.25 , 0.25 ] in corotating orbits.